mlsanityData to 14 Oct 2026

The Alexander-Hirschowitz theorem for neurovarieties

arXiv 2511.19703 ↗First posted 24 Nov 2025math.AG cs.AI cs.LGcited by 6

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Abstract (arXiv)

We study the dimension and identifiability of neurovarieties associated to polynomial neural networks. We give an independent geometric proof that the linear bounds di≥ 2ni-1 on the activation degrees imply non defectiveness for any number of outputs, a dimension statement previously obtained from finite identifiability. The proof is based on a direct analysis of the differential of the parameterization. We also investigate secant and Grassmann-secant obstructions outside this range and prove global identifiability for multi-output architectures under the same degree bounds.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 16 of its 23 references that are in the map. First posted on arXiv 24 Nov 2025.

Builds on

16 of 23 references.

References · 16

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  2. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
  3. 2019On the Expressive Power of Deep Polynomial Neural Networkscited by 66
  4. 2022On the Symmetries of Deep Learning Models and their Internal Representationscited by 64
  5. 2021Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEscited by 43
  6. 2019Pure and Spurious Critical Points: a Geometric Study of Linear Networkscited by 33
  7. 2021Parameter identifiability of a deep feedforward ReLU neural networkcited by 24
  8. 2023Polynomial Neural Fields for Subband Decomposition and Manipulationcited by 22
  9. 2023From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modelingcited by 22
  10. 2021Augmenting Deep Classifiers with Polynomial Neural Networkscited by 21
  11. 2024Geometry of Polynomial Neural Networkscited by 21
  12. 2024Activation degree thresholds and expressiveness of polynomial neural networkscited by 14
4 more
  1. 2024On the Geometry and Optimization of Polynomial Convolutional Networkscited by 11
  2. 2021PolyNet: Polynomial Neural Network for 3D Shape Recognition with PolyShape Representationcited by 9
  3. 2025Learning on a Razor's Edge: Identifiability and Singularity of Polynomial Neural Networkscited by 9
  4. 2021The Landscape of Multi-Layer Linear Neural Network From the Perspective of Algebraic Geometrycited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Identifiable Equivariant Networks are Layerwise Equivariantcited by 7
  2. 2026Rational Neural Networks have Expressivity Advantagescited by 2
  3. 2026The Geometry of Polynomial Group Convolutional Neural Networkscited by 2
  4. 2026Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defectscited by 1
  5. 2026Singular Learning and Occam's Razor in Deep Monomial Networkscited by 0
  6. 2026Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networkscited by 0